TfL has pledged to do "everything we can to support the families and all those affected".
An interim report into the crash is due to be published on Wednesday, but it could take "many months" to produce a final report, investigators warned.
Announcing the offer of assistance to victims' families, London's Transport Commissioner Mike Brown said: "The TfL Sarah Hope line is available 24 hours a day to provide advice on a whole range of matters and immediate financial and other support.
"This includes covering funeral costs and travel expenses for relatives."
Meanwhile, the Rail Accident Investigation Branch (RAIB) has conducted preliminary analysis and downloaded information from the tram's "black box" data recorder.
Previously it said the vehicle had exceeded the speed limit on the bend.
The RAIB said last week the two-carriage tram had been travelling "significantly" faster than the permitted 12mph (19km/h) as it entered a tight bend near the Sandilands stop.
CROYDON TRAM WAS TRAVELLING 3.5 TIMES THE SPEED LIMIT
The Croydon tram was travelling three times the speed limit when it derailed, a report has revealed.
It was was travelling at 43.5 mph on a curve with a speed limit of 12.5mph, the Rail Accident Investigation Branch said in its interim report into the crash.
Transport for London has imposed Temporary speed restrictions on the area of track near the Croydon tram crash.
Update from TfL
TfL: Temporary speed restrictions on Croydon tram
Transport for London has imposed temporary speed restrictions on the area of track near the Croydon tram crash
Our engineers have now repaired all track and other equipment and have run trams over the repaired section.
We will follow the RAIB’s advice and, before service is resumed, will implement additional temporary speed restrictions and associated signage near Sandilands to supplement existing safety arrangements.
We are continuing to carry out a thorough safety assessment and are taking the advice of an independent panel of tram experts. We will only resume services for the local community once that rigorous assurance process has been completed.